Separable Differential Equation

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March 25th 2010, 12:54 PM
littlesohi

Separable Differential Equation

I am confunsed with this problem:

$dy/dx=y + 1/y^2$

would it be:
$\int y^2(y-dy) = \int dt$ ?
March 25th 2010, 12:56 PM
General

Quote:

Originally Posted by littlesohi

I am confunsed with this problem:

$dy/dx=y + 1/y^2$

would it be:
$\int y^2(y-dy) = \int dt$ ?

I do not know what the hell is dt ?!

It will be:
$\frac{dy}{y+\frac{1}{y^2}}=dx$ ..

NOTE: There is a sub-forum for the differential equations ..
March 25th 2010, 01:25 PM
littlesohi

Yeah i'm sorry it should be dx. But the derivative of the left side would be what you said? I know that the right side would be just x, but I don't know how to resolved for the left side.
March 25th 2010, 01:26 PM
General

Quote:

Originally Posted by littlesohi

But the derivative of the left side would be what you said?

I did not say anything about the derivatives ..
March 25th 2010, 02:39 PM
littlesohi

I mean the integral, sorry I'm working on other problems also and I'm gnow a mess. Can you help me with the left side please?
March 25th 2010, 03:17 PM
General

Quote:

Originally Posted by littlesohi

I mean the integral, sorry I'm working on other problems also and I'm gnow a mess. Can you help me with the left side please?

Multiply the integrand by $\, \frac{y^2}{y^2}$ to get :
$\int \frac{y^2}{y^3+1} \, dy$ .. which is easy ..

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